Analysis of correlation matrices usi̇ng the cayley-hamilton theorem: some applications in livestock data

This work employed the Cayley–Hamilton Theorem to perform operations on various powers of a 4 × 4 square matrix. Following a literature research, Pearson correlation coefficients were calculated to analyse the correlations among the morphological traits of Pelibuey sheep in Colima, Mexico. The morphological factors examined for these sheep comprise withers height (WIH), chest girth (CHG), chest width (CHW), and body length (BOL). The computed correlation coefficients between these variables ranged from 0.23 to 0.83. The calculation of higher-order powers of the resulting correlation matrices was streamlined by determining their eigenvalues. In connection to these eigenvalues, many matrices were derived by computing the higher-order powers, square roots, cube roots, sine, cosine, tangent, logarithm, and exponential functions of the 4 × 4 correlation matrices. High ‒ order operations and matrices of diverse polynomials and complex functions, which are otherwise challenging to acquire, were effectively produced utilising the Cayley ‒ Hamilton Theorem. Keywords: Cayley-Hamilton Theorem, Matrix, Determinant, Eigenvalue, Correlation.